NCERT Class 12 · Ch 1 Miscellaneous Exercise · Q7
NCERT Class 12 Maths · Chapter 1 Relations And Functions · Miscellaneous Exercise Question 7
On A={1,2,3}, how many equivalence relations contain (1,2)?
💡 Concept Hints
- Think of equivalence classes rather than choosing ordered pairs independently.
- Write the defining condition carefully and preserve every domain restriction while simplifying.
✅ Step-by-Step Solution
Final Answer: B: 2.
- Equivalence relations correspond to partitions of A. The pair (1,2) forces 1 and 2 into the same block.
- The third element can either form its own block or join their block. The partitions are {{1,2},{3}} and {{1,2,3}}.
- Each partition yields exactly one equivalence relation, giving two in total. Select B.
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